Subjects mechanics

Compressive Stress Cad986

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1. **State the problem:** We need to find the maximum compressive stress a square column can support given a downward force of 281,500 N and a side length of 7 inches. 2. **Formula used:** Compressive stress $\sigma$ is given by the formula: $$\sigma = \frac{F}{A}$$ where $F$ is the force and $A$ is the cross-sectional area. 3. **Calculate the area:** Since the column is square with side length 7 inches, the area is: $$A = 7 \text{ in} \times 7 \text{ in} = 49 \text{ in}^2$$ 4. **Convert area to square meters:** 1 inch = 0.0254 meters, so $$A = 49 \times (0.0254)^2 = 49 \times 0.00064516 = 0.03161384 \text{ m}^2$$ 5. **Calculate compressive stress in Pascals:** $$\sigma = \frac{281,500}{0.03161384} = 8,900,000 \text{ Pa}$$ 6. **Convert Pascals to MPa:** $$8,900,000 \text{ Pa} = 8.9 \text{ MPa}$$ 7. **Final answer:** The maximum compressive stress the column can support is **8.9 MPa**.